Note that for \(n=2\)  the system is underdetermined, hence as in [1]} one should add one more
linear equationIn the general case \({f}={f}(x,{y},\dot{{y}})\)  the operator \(A\mapsto A^{\prime }\)  of §REF 
should be used instead of \(\frac{d}{dx}\) ., namely \(\bigl (\tfrac{d^2}{dx^2}A_i^k\bigr )\phi _{kj}=\bigl (\tfrac{d^2}{dx^2}A_j^k\bigr )\phi _{ki}\) .
Then we get the \(3\times 3\)  matrix of the system, which is generically nondegenerate, whence the same conclusion.
